French Socialist party leader Martine Aubry speaks to the media after a US judge released Dominique Strauss-Kahn from house arrest. Photograph: Philippe Huguen/AFP/Getty Images

Martine Aubry, a challenger for the Socialist ticket in next year's French presidential election, has threatened legal action over allegations that her husband is an Islamist and denounced rumours that she has suffered from alcoholism.

Politicians on the left have long warned that the 2012 French presidential race risked descending into a battle of personal smear campaigns. Charges of attempted rape against the former Socialist frontrunner Dominique Strauss-Kahn in New York and a new legal complaint over an alleged attempted rape in France, as well as stories on his wealth and pursuit of women, have intensified the scrutiny of presidential hopefuls.

Aubry, the Socialist leader and mayor of Lille, threatened to sue websites which did not remove references to her husband, the lawyer Jean-Louis Brochen, as an "Islamist" or "Salafist".

In 1993, before France's law banning religious symbols in schools, Brochen defended schoolgirls threatened with exclusion for wearing headscarves and a Jewish boy who wore a skull cap. Brochen, a staunch secularist, has said it was a lawyer's role to defend all sorts of cases.

The Journal du Dimanche reported that Aubry made telephone warnings to people she suspected of slandering her husband or spreading rumours that she had fought alcoholism or suffered health problems. These included a former minister under Jacques Chirac and a senior figure at the Elysée. The paper said one former government minister had said in private, without producing proof, that Aubry had undergone two detox treatments for alcohol use in a clinic in the south of France.

Socialists suspect the Elysée and Nicolas Sarkozy's ruling rightwing UMP party of stoking gossip against Aubry. This charge was rejected outright by Nadine Morano, minister for learning and vocational training, who said Aubry was portraying herself as a victim to detract from the shortcomings of the Socialist campaign.

The former rightwing prime minister Dominique de Villepin, who also has ambitions to challenge Sarkozy for the presidency, said rumours about Aubry were "scandalous" and "foul" and warned that no one should play dirty politics.

The latest poll, for Ifop, found that 46% of French people felt the Socialist François Hollande was most capable of beating Sarkozy, followed by Aubry on 27%.